Spin-Polarized Fractional Corner Charges and Their Photonic Realization.

We demonstrate that a spin degree of freedom can introduce additional texture to higher order topological insulators (HOTIs), manifesting in novel topological invariants and phase transitions. Spin-polarized mid-gap corner states of various multiplicities are predicted for different HOTI phases, and novel bulk-boundary correspondence principles are defined based on bulk invariants such as total and spin corner charge. Those are shown to be robust to spin-flipping perturbations. Photonic realizations of spin-linked topological phases are demonstrated in engineered systems using pseudospin.